Description

The SIMPLEX method is a single-shot method which attempts to find the local fit-statistic minimum nearest to the starting point. Its principal advantage is that it can work well with complicated statistic surfaces (more so than LEVENBERG-MARQUARDT), while also working quickly (more so than POWELL). Its principal disadvantages are that it has a tendency to ``get stuck'' in regions with complicated topology before reaching the local fit-statistic minimum, and that there is no guarantee it will find the global fit-statistic minimum. Its tendency to stick means that the user may be best-served by repeating fits until the best-fit point does not change.

A simplex is geometrical form in N-dimensional in parameter space which has N + 1 vertices (e.g., in 3-D it is a tetrahedron). The fit statistic is evaluated for each vertex, and one or more points of the simplex are moved, so that the simplex moves towards the nearest local fit-statistic minimum. When a minimum is reached, the simplex may also contract itself, as an amoeba might; hence, the routine is also sometimes called ``amoeba.'' Convergence is reached when the simplex settles into a minimum and all the vertices are within some value eps of each other.

The eps parameter controls when the optimization will cease; for SIMPLEX, this will occur when

| S_i - S_(i-1) | < eps ,

where S_(i-1) and S_i are the observed statistic values for the (i-1)th and ith iteration, respectively.